Perturbative calculations of entanglement entropy

A bstract This paper is an attempt to extend the recent understanding of Page curve for evaporating black holes more general systems coupled a heat bath. Although calculating von Neumann entropy by replica trick usually challenge, we have identified two solvable cases. For initial section curve, sum up perturbation series in system-bath coupling ? ; most interesting contribution order 2 s , where number replicas. saturated regime, consider effect external impulse on at later time and relate it OTOCs. significant simplification occurs maximal chaos case such that may be interpreted terms intermediate object, analogous branching surface wormhole.